Wilfried Meyer-Viol

We offer a formal account of the English past tenses. We see the perfect as having reference time at speech time and the preterite as having reference time at event time. We formalize four constraints on reference time, which we bundle together under the term ‘perspective’. Once these constraints are satisfied at the different reference times of the perfect and preterite, the contrasting functions of these tenses are explained. Thus we can account formally for the ‘definiteness effect’ and the ‘lifetime effect’ of the perfect, for the fact that the perfect seems to ‘explain’ something about the present, and that the perfect cannot presuppose a past time point. We explain why perfect and preterite can sometimes be interchangeable, and we offer a solution to the ’present perfect puzzle’. We explain the unacceptability of notorious examples of the perfect such as * Gutenberg has discovered the art of printing . We give greater definition to the familiar notions of ‘current relevance’ and ‘extended now’

A modal logic is developed to deal with finite ordered binary trees a they are used in linguistics. A modal language is introduced with operators for the ‘mother of’, ‘first daughter of’ and ‘second daughter of’ relations together with their transitive reflexive closures. The relevant class of tree models is defined and three linguistic applications of this language are discussed: context free grammars, command relations, and trees decorated with feature structures. An axiomatic proof system is given for which completeness is shown with respect to the class of finite ordered binary trees. A number of decidability results follow